1 Introduction

In any competitive sport there is a natural desire to know who the best is. However, in boxing the rankings have been criticized as criminally suspect. Spoiled by monetary incentives, boxing promoters often create mismatched bouts to inflate their boxer’s records. Also, there are 5 sanctioning organizations that award titles in trivialized weight classes resulting in the potential of over a 100 boxer’s named as “world champion” at any one time.

In this document I describe an objective method to rank boxers and to determine who is the best current heavyweight boxer. I structure boxers into a network and use Google’s PageRank algorithm to quantify which boxer is the most important in the network. The graph below shows the network of boxers where the links between them represent a boxing match outcome between the fighters and the size of a boxer’s name is proportional to his rank.

2 Data Collection

The win / loss record of the top 50 current heavyweight boxers as ranked by boxrec.com was extracted from Wikipedia.com. These boxers were chosen mainly for convenience. Ideally, I would have liked to have a chained sample with the top 50 boxers as seeds but that proved difficult to obtain. With the convenience sample, boxers in the network won’t get as much credit for defeating some of their opponents but that’s an acceptable compromise because a boxer that isn’t ranked in the top 50 are likely not very good. Only current active heavyweight boxers were sampled because boxers from different weight classes and eras are unlikely to be linked together.

3 Network Definition

The network contains 783 nodes and 1075 links / edges. Each node represents one of the top 50 heavyweight boxers or a boxer that they defeated. The directed links represent a boxing match that resulted in a win going from the losing boxer to the winning boxer. The weights of the links are based on the type of resulting win. If the win was more definite (e.g. knockout) it was weighted higher than a win that’s more open to interpretation (e.g. split decision).

4 Boxer’s Rankings

Google’s PageRank algorithm was used to rank the boxers in the network. The algorithm is the most well-known method that Google’s search engine used to rank webpages in search results. It was designed so that webpages that received a lot of links from other webpages that received a lot of links would be ranked higher. It’s appropriate for the network of boxers because boxers that defeated other quality boxers should be ranked higher. The damping factor of the algorithm was set to 0.999 so that boxers with more quality wins “absorb” more of the importance in the network and are ranked higher.

4.1 Analysis of Rankings

The top 5 boxers in the network is displayed in the bar chart above. The results are reasonable except for the notable exclusion of Tyson Fury. He is rightfully in anyone’s top 5 list but is ranked number 22 by the algorithm. The main reason for his lower ranking is because the network doesn’t account for his defeat of Wladimir Klitschko. Klitschko was dominate in his era and including him in the sample would have advanced Tyson Fury to be ranked second.

Also, the algorithm assigns too much importance to boxers with a lot of wins against low quality boxers. For example, Tomasz Adamek is ranked number 10 because he has 51 links / wins, but those links are to boxers that don’t have incoming links to them. Eric Molina knocked out Adamek but Molina is ranked lower at 17 because he only has 24 links. I believe some these issues would be solved if a larger sample was used which would result in a network that’s more interconnected (current network density: 0.0018).

5 Conclusion

An objective ranking of boxers creates more credibility and interest for the sport. I applied Google’s PageRank algorithm to rank current heavyweight boxers and the results were mostly consistent with intuition. A larger sample of boxers and some modifications to the algorithm could provide more reasonable rankings.

6 Code

6.1 (click “Code” button to show/hide code)

Load libraries

LoadPackages <- function(packages) {
  # Load or install packages if they aren't already loaded.
  #
  # Args:
  #   packages: a vector of package names
  #
  for (package in packages) {
    if (!require(package, character.only=T, quietly=T)) {
      if (!package %in% installed.packages()) install.packages(package)
      library(package, character.only=T)
    }
  }
}

LoadPackages(c("rvest", "dplyr", "tibble", "stringr", "igraph", "networkD3",
               "ggplot2"))

Urls that contain boxer’s record

urls = c('https://en.wikipedia.org/wiki/Anthony_Joshua',
         'https://en.wikipedia.org/wiki/Deontay_Wilder',
         'https://en.wikipedia.org/wiki/Tyson_Fury',
         'https://en.wikipedia.org/wiki/Dillian_Whyte', 
         'https://en.wikipedia.org/wiki/Alexander_Povetkin',
         'https://en.wikipedia.org/wiki/Jarrell_Miller',
         'https://en.wikipedia.org/wiki/Kubrat_Pulev',
         'https://en.wikipedia.org/wiki/Luis_Ortiz_(Cuban_boxer)',
         'https://en.wikipedia.org/wiki/Dominic_Breazeale',
         'https://en.wikipedia.org/wiki/Adam_Kownacki',
         'https://en.wikipedia.org/wiki/Óscar_Rivas',
         'https://en.wikipedia.org/wiki/Joseph_Parker_(boxer)',
         'https://en.wikipedia.org/wiki/Agit_Kabayel',
         'https://en.wikipedia.org/wiki/Filip_Hrgović',
         'https://en.wikipedia.org/wiki/Sergei_Kuzmin_(boxer)',
         "https://en.wikipedia.org/wiki/Joe_Joyce_(boxer)",
         "https://en.wikipedia.org/wiki/Andy_Ruiz",
         "https://en.wikipedia.org/wiki/Dereck_Chisora",
         "https://en.wikipedia.org/wiki/Nathan_Gorman_(boxer)",
         "https://en.wikipedia.org/wiki/Evgenyi_Romanov",
         "https://en.wikipedia.org/wiki/Christian_Hammer",
         "https://en.wikipedia.org/wiki/Robert_Helenius",
         "https://en.wikipedia.org/wiki/Efe_Ajagba",
         "https://en.wikipedia.org/wiki/Bryant_Jennings",
         "https://en.wikipedia.org/wiki/Charles_Martin_(boxer)",
         "https://en.wikipedia.org/wiki/Lucas_Browne",
         "https://en.wikipedia.org/wiki/Marco_Huck",
         "https://en.wikipedia.org/wiki/Hughie_Fury",
         "https://en.wikipedia.org/wiki/Carlos_Takam",
         "https://en.wikipedia.org/wiki/Tomasz_Adamek",
         "https://en.wikipedia.org/wiki/Junior_Fa",
         "https://en.wikipedia.org/wiki/Kyotaro_Fujimoto",
         "https://en.wikipedia.org/wiki/Johann_Duhaupas",
         "https://en.wikipedia.org/wiki/Tony_Yoka",
         "https://en.wikipedia.org/wiki/Artur_Szpilka",
         "https://en.wikipedia.org/wiki/Zhang_Zhilei",
         "https://en.wikipedia.org/wiki/Alexander_Dimitrenko",
         "https://en.wikipedia.org/wiki/Simon_Kean",
         "https://en.wikipedia.org/wiki/Mariusz_Wach",
         "https://en.wikipedia.org/wiki/Trevor_Bryan",
         "https://en.wikipedia.org/wiki/Éric_Molina",
         "https://en.wikipedia.org/wiki/Bogdan_Dinu",
         "https://en.wikipedia.org/wiki/Izu_Ugonoh",
         "https://en.wikipedia.org/wiki/Arnold_Gjergjaj",
         "https://en.wikipedia.org/wiki/Tyrone_Spong",
         "https://en.wikipedia.org/wiki/Franz_Rill",
         "https://en.wikipedia.org/wiki/George_Arias_(boxer)",
         "https://en.wikipedia.org/wiki/Erkan_Teper",
         "https://en.wikipedia.org/wiki/Gerald_Washington_(boxer)",
         "https://en.wikipedia.org/wiki/Demsey_McKean")

Extract boxer’s name from urls

boxer_names <- str_replace_all(urls, '.+wiki\\/', '') %>% 
  str_replace_all('_', ' ') %>% str_replace_all(' \\(.+', '')

Extract boxer’s win/loss record

# col names that indentifies a win/loss record table
req_names = c("Result", "Record", "Opponent")

record_lst = list()

# for each boxer extract win/loss record form wikipedia url
for (i in 1:length(urls)){
  # read tables on webpage
  tbl <- read_html(urls[i]) %>% 
    html_nodes(css = 'table')
  
  # for each table check if it's the win/loss record
  for (j in 1:length(tbl)){
    # convert html table to dataframe
    record_temp = tbl[j] %>% html_table(fill = TRUE) %>% as.data.frame()
    # check if the names in table look like a table with win/loss record 
    if(length(intersect(req_names, record_temp %>% names())) == 3) {
      # save the win/loss record to a list of records
      record_lst[[i]] <- record_temp %>%
        # create col for boxer's name
        mutate(boxer = boxer_names[i])
      # break out of loop because record was found
      break
    }
    # vector of values for fist row
    row1 <- record_temp %>% slice(1) %>% unlist(.,use.names = F)
    # if the first row looks like col names of record table
    if(length(intersect(req_names, row1)) == 3){
      # use the first row values as col names
      names(record_temp) <- row1
      # remove first first row
      record_temp <- record_temp[-1,]
      # save the win/loss record to a list of records
      record_lst[[i]] <- record_temp %>%
        # create a col for boxer's name
        mutate(boxer = boxer_names[i],
               `No.` = as.integer(`No.`))
      # break out of loop because record was found
      break
    }
  }
}

Filter records for wins only

# remove null entries from list
# some boxers may not have win/loss records on their wikipeida page
record_lst <- record_lst[!sapply(record_lst, is.null)]

# saveRDS(record_lst, "../data/record_lst.rds")
# record_lst <- readRDS("../data/record_lst.rds")

record_df <- bind_rows(record_lst) %>% 
  # only wins 
  filter(Result %in% c("Win")) #%>% 
  # filter for only wins against other top boxers
  #filter(Opponent %in% boxer_names) # might re-consider this

# includeing draws makes Fury and Wilder completely dominate the network
# based on PR scores

# boxer's records that weren't available
# setdiff(boxer_names, unique(record_df$boxer))

Create network graph object

relations <- record_df %>% 
  # centrality measure gives importance to nodes with more edges directed toward
  # a node. Therefore, relationships is defined as opponent gives a loss to boxer
  mutate(to = boxer, from = Opponent) %>%
  select(from, to, Result, Type) %>%
  # create weights for different win outcomes
  # weights don't appear to affect page rank much
  mutate(weight = 
           case_when(#Result == "Draw" ~ .5,
                     Result == "Win" & Type %in% c("DQ", "TD") ~ 1,
                     Result == "Win" & Type %in% c("SD", "DEC") ~ 1.25,
                     Result == "Win" & Type %in% c("PTS", "MD") ~ 1.5,
                     Result == "Win" & Type %in% c("UD") ~ 1.75,
                     Result == "Win" & Type %in% c("TKO", "KO", "RTD") ~ 2)) %>%
  # sum the weights and remove dupes
  group_by(from, to) %>%
  mutate(weight = sum(weight), rn = row_number()) %>%
  ungroup() %>% 
  filter(rn == 1) %>%
  select(from, to, weight)

# names of boxers in sample
boxers_df = data.frame(name = union(relations$to, relations$from))

# create igraph object
boxers_g <- graph_from_data_frame(relations, directed = T, vertices = boxers_df)

# save igraph object. to be plotted using gephi
# write_graph(boxers_g, file = '../data/boxers_g.gml', format = 'gml')

Ranking

# page rank centrality
# PageRank theory suggests that an imaginary flow of losses that is randomly
# going from one boxer to another will eventually stop. The damping factor is
# the probability that the flow will continue at any step. Setting the damping
# factor to 1 implies the flow of random losses will continue and when its 
# applied to the network it will end on a boxer with no losses making that 
# boxer's importance higher. Boxer's with no losses "absorb" more of the 
# importance from boxer's that they beat. (AJ has higher
# page rank value when damping is set to 1. When damping = 0 then they all have
# the same value)
# boxers aren't directly penalized for losses but the PR values sum up to 1 so
# when another boxer's PR value increases from wins other boxers value goes down
pr <- page_rank(boxers_g, algo = "prpack", vids = V(boxers_g),
                directed = TRUE, damping = .9999) # damping = 1 wont converge

# create a dataframe of boxer's ranking and sort 
ranking <- pr$vector %>% 
  as.data.frame() %>% 
  rownames_to_column("Boxer") %>%
  rename(Page_Rank = 2) %>%
  arrange(desc(Page_Rank)) %>%
  mutate(RN = row_number()) %>%
  select(RN, Boxer, Page_Rank) %>%
  left_join(relations %>%
  group_by(to) %>%
  summarize(Wins = n()), by = c("Boxer" = "to"))

# saveRDS(ranking, "../data/ranking.rds")

ranking

D3 network graph

V(boxers_g)$div=c("Boxers")
# delete any vertices that have no edges attached.
boxers_g <- delete.vertices(boxers_g,degree(boxers_g)==0)
# create ids
nodes <- data.frame(vertex_attr(boxers_g))
nodes$ID <- as.numeric(nodes$name)-1
# data frame with edge list
edges <- data.frame(get.edgelist(boxers_g)) 
colnames(edges) <- c("source","target")

edges <- merge(edges, nodes[,c("name","ID")],by.x="source",by.y="name")
edges <- merge(edges, nodes[,c("name","ID")],by.x="target",by.y="name")
edges <- edges[,3:4]
colnames(edges)=c("source","target")


j <- forceNetwork(Links=edges, Nodes=nodes, Source = "source",
                  Target = "target", NodeID="name", Group="div",
                  fontSize=12, opacity = 0.8, zoom=T, legend=T)

j

# saveNetwork(j, file = '../data/boxers_d3.html')

Application of Google’s PageRank to Pro Boxers

Tommy Lang

3/15/19